Question

QUESTION 9 A bag contains 1 green marbles and 3 red marbles. 6 times a marble is removed from the bag, its color noted, and then returned Success is getting a green marble. Find the probability of getting three green marbles. Round off to three decimal places.

Answer 1

Bag contain 1 green and 3 red marbles out of the total of 4 marbles

Getting a green marble is treated as success.

Marbles are removed from the bag with replacement.

Then P(success)=P(getting green marble) = 1/4 =0.25 [ because bag contains only one green marble out of 4 total 4 marbles]. This probability remains same in each removal of marble from the bag.

Remaval performed 6 times.

Let X denote the number of successes in these 6 removals ( ie, number of times getting green marbles)

Then X follow Binomial distribution with parameters 6 and 0.25

Then

$P(X=x)=\binom{6}{x}(0.25)^{x}(1-0.25)^{6-x},x=0,1,2,3,4,5,6$

Now the probability of getting 3 green marbles out of the 6 removals, or probability of getting 3 successes out of the 6 removals is P(X=3). This is

$P(X=3)=\binom{6}{3}(0.25)^{3}(1-0.25)^{6-3}$

  

= 20 X 0.015625 x 0.421875 = 0.132